The dynamics of a system determine how the system moves in response to internal or external forces applied in different states. Effective control of a system is dependent on having an accurate model of the system's dynamics. Effective predictive filtering is similarly dependent on having an accurate model of the dynamics of the system under observation.
An accurate model of system dynamics is able to capture how different perturbations affect the system. This model should also capture how internal dynamics, such as the inertia between coupled components, cause the system to move. The model can be used to generate control signals to move the system in a desired way and/or prediction signals to predict a future state of a system under observation.
Effective control or predictive filtering also requires a system model that is able to effectively account for kinematic changes in the system. For example, when a robotic arm manipulates an objects of unknown dimensions or at an unknown gripping point, the overall kinematics and dynamics of the robotic arm change. Similarly, when parameters of the system change, for example due to degradation over time, the dynamics and possibly the kinematics of the system will change. A system model that is able to automatically and effectively account for changes in both kinematics and dynamics will provide more accurate control and prediction for a broader range of systems.
Effective adaptive control and predictive filtering in systems becomes increasingly complex as the degrees of freedom in the system increase. The complexity of the models needed to account for system dynamics increases with the dimensions of the system. Nonlinear models have great potential for accurately modelling a system, but are also more complicated to develop.
Previous approaches to nonlinear adaptation use nonlinear components that give multidimensional outputs, for which there is a single coefficient that is learned. This approach is subject to the curse of dimensionality for high degree of freedom systems, as the number of bases required to tile the state space increases exponentially with the degrees of freedom of the system. These methods also cannot be directly applied using hardware components that communicate using scalar outputs. A system design that is able to provide effective adaptive control and predictive filtering and can scale to higher degrees of freedom would be beneficial. Such a design could provide more efficient implementations of nonlinear adaptive control/prediction and allow a wider range of hardware implementations.